Mach's principle is considered falls by many because mass anisotropy would not be consistent with the Huges-Drever experiments, which showed the isotropy of nuclear resonance. However, anisotropy appears as well in GR in the form of radial length contraction, which can be interpreted as increase of inertia in the radial direction (the observer at infinity can not tell the difference). Thus one would expect anisotropic behavior of mass in GR just the same as according to Mach's principle. The fact that GR time dilation is isotropic does not change this anisotropic aspect of GR. So why is it an issue within Mach's principle and not within GR? I tried to find a resource on a GR harmonic oscillator, but I can not find a paper that answers this question really. Thanks for your input!